WORKING PAPERS F/ FUND ACCOUNTING
WORKING PAPERS F/ FUND ACCOUNTING
22nd Edition
ISBN: 9781308868394
Author: Wild
Publisher: MCG CUSTOM
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Question
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Chapter B, Problem 11E
To determine

Compound Interest is the interest which is calculated on the initial principal amount as well as on the interest that is accumulated. Compound interest can be compounded annually, compounded semi annually, compounded quarterly, monthly, daily etc.

To Determine:-

Here, in the problem provided to us, we are required to ascertain the initial amount that Otto co. can borrow if there are four payments of $13, 000 each and the interest rate is 8% or 12% or 16% compounded semi annually.

Expert Solution & Answer
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Answer to Problem 11E

Solution:-

When the compounding is done semi annually the interest rate is divided by two, since there are two periods in the year when the interest would be charged.

In the given problem, we have been asked to provide the amount which Otto co. can borrow at various interest rates compounded semi annually.

When the interest rate is 8% compounded semi annually, the Otto can borrow $47189.
When the interest rate is 12% compounded semi annually, the Otto can borrow $45046.
When the interest rate is 16% compounded semi annually, the Otto can borrow $43058.

Explanation of Solution

Explanation:-

Following formula has been used:

    Amount=Principal(1+Rate)n

, Where n is the number of periods compounded.

Now, when the interest rate is 8% compounded semi annually, then the amount that Otto co. can borrow is as follows:-

    =13000( 1.04)+13000( 1.04)2+13000( 1.04)3+13000 ( 1.04 ) 4

    =$47, 189

It can be proved with an amortisation table:-

    Date
    Opening balance
    Interest Amount @4%
    Principal Amount
    Closing Balance
    01-11-2015
    47189
    1887.56
    11112.44
    36076.56
    01-05-2016
    36077
    1443
    11557
    24520
    01-11-2016
    24520
    981
    12019
    12500
    01-05-2017
    12500
    500
    12500
    0

Now, when the interest rate is 12% compounded semi annually, then the amount that Otto co. can borrow is as follows:-

    =13000( 1.06)+13000( 1.06)2+13000( 1.06)3+13000 ( 1.06 ) 4

    =$45, 046

It can be proved with an amortisation table:-

    Date
    Opening balance
    Interest Amount @6%
    Principal Amount
    Closing Balance
    01-11-2015
    45046
    2702.76
    10297.24
    34748.76
    01-05-2016
    34749
    2085
    10915
    23834
    01-11-2016
    23834
    1430
    11570
    12264
    01-05-2017
    12264
    736
    12264
    0

Now, when the interest rate is 16% compounded semi annually, then the amount that Otto co. can borrow is as follows:-

    =13000( 1.08)+13000( 1.08)2+13000( 1.08)3+13000 ( 1.08 ) 4

    =$43, 058

It can be proved with an amortisation table:-

    Date
    Opening balance
    Interest Amount @8%
    Principal Amount
    Closing Balance
    01-11-2015
    43058
    3444.64
    9555.36
    33502.64
    01-05-2016
    33503
    2680
    10320
    23183
    01-11-2016
    23183
    1855
    11145
    12037
    01-05-2017
    12037
    963.0
    12037
    0

Conclusion

Conclusion:-

As can be seen that with the increase in interest rate the amount that Otto co. can borrow is decreasing, since it has to pay more interest on the same amount.

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